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Reddit mentions of Mathematical Methods for Physicists: A Comprehensive Guide

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We found 8 Reddit mentions of Mathematical Methods for Physicists: A Comprehensive Guide. Here are the top ones.

Mathematical Methods for Physicists: A Comprehensive Guide
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Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples.Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises.
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Found 8 comments on Mathematical Methods for Physicists: A Comprehensive Guide:

u/dargscisyhp · 7 pointsr/AskScienceDiscussion

I'd like to give you my two cents as well on how to proceed here. If nothing else, this will be a second opinion. If I could redo my physics education, this is how I'd want it done.

If you are truly wanting to learn these fields in depth I cannot stress how important it is to actually work problems out of these books, not just read them. There is a certain understanding that comes from struggling with problems that you just can't get by reading the material. On that note, I would recommend getting the Schaum's outline to whatever subject you are studying if you can find one. They are great books with hundreds of solved problems and sample problems for you to try with the answers in the back. When you get to the point you can't find Schaums anymore, I would recommend getting as many solutions manuals as possible. The problems will get very tough, and it's nice to verify that you did the problem correctly or are on the right track, or even just look over solutions to problems you decide not to try.

Basics

I second Stewart's Calculus cover to cover (except the final chapter on differential equations) and Halliday, Resnick and Walker's Fundamentals of Physics. Not all sections from HRW are necessary, but be sure you have the fundamentals of mechanics, electromagnetism, optics, and thermal physics down at the level of HRW.

Once you're done with this move on to studying differential equations. Many physics theorems are stated in terms of differential equations so really getting the hang of these is key to moving on. Differential equations are often taught as two separate classes, one covering ordinary differential equations and one covering partial differential equations. In my opinion, a good introductory textbook to ODEs is one by Morris Tenenbaum and Harry Pollard. That said, there is another book by V. I. Arnold that I would recommend you get as well. The Arnold book may be a bit more mathematical than you are looking for, but it was written as an introductory text to ODEs and you will have a deeper understanding of ODEs after reading it than your typical introductory textbook. This deeper understanding will be useful if you delve into the nitty-gritty parts of classical mechanics. For partial differential equations I recommend the book by Haberman. It will give you a good understanding of different methods you can use to solve PDEs, and is very much geared towards problem-solving.

From there, I would get a decent book on Linear Algebra. I used the one by Leon. I can't guarantee that it's the best book out there, but I think it will get the job done.

This should cover most of the mathematical training you need to move onto the intermediate level physics textbooks. There will be some things that are missing, but those are usually covered explicitly in the intermediate texts that use them (i.e. the Delta function). Still, if you're looking for a good mathematical reference, my recommendation is Lua. It may be a good idea to go over some basic complex analysis from this book, though it is not necessary to move on.

Intermediate

At this stage you need to do intermediate level classical mechanics, electromagnetism, quantum mechanics, and thermal physics at the very least. For electromagnetism, Griffiths hands down. In my opinion, the best pedagogical book for intermediate classical mechanics is Fowles and Cassidy. Once you've read these two books you will have a much deeper understanding of the stuff you learned in HRW. When you're going through the mechanics book pay particular attention to generalized coordinates and Lagrangians. Those become pretty central later on. There is also a very old book by Robert Becker that I think is great. It's problems are tough, and it goes into concepts that aren't typically covered much in depth in other intermediate mechanics books such as statics. I don't think you'll find a torrent for this, but it is 5 bucks on Amazon. That said, I don't think Becker is necessary. For quantum, I cannot recommend Zettili highly enough. Get this book. Tons of worked out examples. In my opinion, Zettili is the best quantum book out there at this level. Finally for thermal physics I would use Mandl. This book is merely sufficient, but I don't know of a book that I liked better.

This is the bare minimum. However, if you find a particular subject interesting, delve into it at this point. If you want to learn Solid State physics there's Kittel. Want to do more Optics? How about Hecht. General relativity? Even that should be accessible with Schutz. Play around here before moving on. A lot of very fascinating things should be accessible to you, at least to a degree, at this point.

Advanced

Before moving on to physics, it is once again time to take up the mathematics. Pick up Arfken and Weber. It covers a great many topics. However, at times it is not the best pedagogical book so you may need some supplemental material on whatever it is you are studying. I would at least read the sections on coordinate transformations, vector analysis, tensors, complex analysis, Green's functions, and the various special functions. Some of this may be a bit of a review, but there are some things Arfken and Weber go into that I didn't see during my undergraduate education even with the topics that I was reviewing. Hell, it may be a good idea to go through the differential equations material in there as well. Again, you may need some supplemental material while doing this. For special functions, a great little book to go along with this is Lebedev.

Beyond this, I think every physicist at the bare minimum needs to take graduate level quantum mechanics, classical mechanics, electromagnetism, and statistical mechanics. For quantum, I recommend Cohen-Tannoudji. This is a great book. It's easy to understand, has many supplemental sections to help further your understanding, is pretty comprehensive, and has more worked examples than a vast majority of graduate text-books. That said, the problems in this book are LONG. Not horrendously hard, mind you, but they do take a long time.

Unfortunately, Cohen-Tannoudji is the only great graduate-level text I can think of. The textbooks in other subjects just don't measure up in my opinion. When you take Classical mechanics I would get Goldstein as a reference but a better book in my opinion is Jose/Saletan as it takes a geometrical approach to the subject from the very beginning. At some point I also think it's worth going through Arnold's treatise on Classical. It's very mathematical and very difficult, but I think once you make it through you will have as deep an understanding as you could hope for in the subject.

u/We_have_no_future · 3 pointsr/PhysicsStudents

Shankar's book teaches almost everything you need: calculus, vectors, series, complex variables, ODE, linear algebra in only ~300pag.
http://www.amazon.com/Basic-Training-Mathematics-Fitness-Students/dp/0306450364


For more advanced topics check out Arfken.

u/isentr0pic · 2 pointsr/AskPhysics

Interdisciplinary connections spring up from generality. You'd be hard pressed to find a spontaneous connection between something like particle phenomenology and an unrelated field.

To illustrate this idea of generality, consider the methods of statistical mechanics, which are so general that they can be used to describe everything from black holes to ferromagnets. However, the methods have also been used to model neural networks and social dynamics (the latter being accurate enough to successfully recreate historical events.)

What makes statistical mechanics more general than other branches? Probably the fact that it's almost more mathematics than physics, specifically a branch of probability theory regarding highly correlated random variables.

With this in mind, perhaps you'd benefit from focusing your attention on the mathematical ideas that drive physics rather than physics itself. Take the calculus of variations which, whilst developed for problems in classical mechanics, has found applications in mathematical optimisation. Another example being brownian motion, the mathematics of which have been generalised to higher dimensions and applied to finance. The mathematics behind relativity is differential geometry, which has been applied to too many fields to list.

I'd recommend having a look at Mathematical Methods for Physicists by Arfken, Weber and Harris for a broad overview of the methods.

u/The_MPC · 2 pointsr/Physics

Rather than list various courses, I'll say this. If you can use all the techniques in this book:

http://www.amazon.com/Mathematical-Methods-Physicists-Seventh-Edition/dp/0123846544/ref=dp_ob_title_bk/185-3957242-1103639

and understand the content of this book:

http://www.amazon.com/Mathematical-Physics-Sadri-Hassani/dp/0387985794/ref=sr_1_1?s=books&ie=UTF8&qid=1335192374&sr=1-1

then you will almost certainly know all they math you'll ever need for advanced undergraduate and general graduate courses. In fact, you'll almost certainly know much more than you'll need.

That's not to say that you should simply study those books - the second one is a gem, but the first is.... polarizing - but they're useful guides of what you ought to know.

u/HQuez · 2 pointsr/AskPhysics

For math you're going to need to know calculus, differential equations (partial and ordinary), and linear algebra.

For calculus, you're going to start with learning about differentiating and limits and whatnot. Then you're going to learn about integrating and series. Series is going to seem a little useless at first, but make sure you don't just skim it, because it becomes very important for physics. Once you learn integration, and integration techniques, you're going to want to go learn multi-variable calculus and vector calculus. Personally, this was the hardest thing for me to learn and I still have problems with it.

While you're learning calculus you can do some lower level physics. I personally liked Halliday, Resnik, and Walker, but I've also heard Giancoli is good. These will give you the basic, idealized world physics understandings, and not too much calculus is involved. You will go through mechanics, electromagnetism, thermodynamics, and "modern physics". You're going to go through these subjects again, but don't skip this part of the process, as you will need the grounding for later.

So, now you have the first two years of a physics degree done, it's time for the big boy stuff (that is the thing that separates the physicists from the engineers). You could get a differential equations and linear algebra books, and I highly suggest you do, but you could skip that and learn it from a physics reference book. Boaz will teach you the linear and the diffe q's you will need to know, along with almost every other post-calculus class math concept you will need for physics. I've also heard that Arfken, Weber, and Harris is a good reference book, but I have personally never used it, and I dont' know if it teaches linear and diffe q's. These are pretty much must-haves though, as they go through things like fourier series and calculus of variations (and a lot of other techniques), which are extremely important to know for what is about to come to you in the next paragraph.

Now that you have a solid mathematical basis, you can get deeper into what you learned in Halliday, Resnik, and Walker, or Giancoli, or whatever you used to get you basis down. You're going to do mechanics, E&M, Thermodynamis/Statistical Analysis, and quantum mechanics again! (yippee). These books will go way deeper into theses subjects, and need a lot more rigorous math. They take that you already know the lower-division stuff for granted, so they don't really teach those all that much. They're tough, very tough. Obvioulsy there are other texts you can go to, but these are the one I am most familiar with.

A few notes. These are just the core classes, anybody going through a physics program will also do labs, research, programming, astro, chemistry, biology, engineering, advanced math, and/or a variety of different things to supplement their degree. There a very few physicists that I know who took the exact same route/class.

These books all have practice problems. Do them. You don't learn physics by reading, you learn by doing. You don't have to do every problem, but you should do a fair amount. This means the theory questions and the math heavy questions. Your theory means nothing without the math to back it up.

Lastly, physics is very demanding. In my experience, most physics students have to pretty much dedicate almost all their time to the craft. This is with instructors, ta's, and tutors helping us along the way. When I say all their time, I mean up until at least midnight (often later) studying/doing work. I commend you on wanting to self-teach yourself, but if you want to learn physics, get into a classroom at your local junior college and start there (I think you'll need a half year of calculus though before you can start doing physics). Some of the concepts are hard (very hard) to understand properly, and the internet stops being very useful very quickly. Having an expert to guide you helps a lot.

Good luck on your journey!

u/sneddo_trainer · 1 pointr/chemistry

Personally I make a distinction between scripting and programming that doesn't really exist but highlights the differences I guess. I consider myself to be scripting if I am connecting programs together by manipulating input and output data. There is lots of regular expression pain and trial-and-error involved in this and I have hated it since my first day of research when I had to write a perl script to extract the energies from thousands of gaussian runs. I appreciate it, but I despise it in equal measure. Programming I love, and I consider this to be implementing a solution to a physical problem in a stricter language and trying to optimise the solution. I've done a lot of this in fortran and java (I much prefer java after a steep learning curve from procedural to OOP). I love the initial math and understanding, the planning, the implementing and seeing the results. Debugging is as much of a pain as scripting, but I've found the more code I write the less stupid mistakes I make and I know what to look for given certain error messages. If I could just do scientific programming I would, but sadly that's not realistic. When you get to do it it's great though.

The maths for comp chem is very similar to the maths used by all the physical sciences and engineering. My go to reference is Arfken but there are others out there. The table of contents at least will give you a good idea of appropriate topics. Your university library will definitely have a selection of lower-level books with more detail that you can build from. I find for learning maths it's best to get every book available and decide which one suits you best. It can be very personal and when you find a book by someone who thinks about the concepts similarly to you it is so much easier.
For learning programming, there are usually tutorials online that will suffice. I have used O'Reilly books with good results. I'd recommend that you follow the tutorials as if you need all of the functionality, even when you know you won't. Otherwise you get holes in your knowledge that can be hard to close later on. It is good supplementary exercise to find a method in a comp chem book, then try to implement it (using google when you get stuck). My favourite algorithms book is Numerical Recipes - there are older fortran versions out there too. It contains a huge amount of detailed practical information and is geared directly at computational science. It has good explanations of math concepts too.

For the actual chemistry, I learned a lot from Jensen's book and Leach's book. I have heard good things about this one too, but I think it's more advanced. For Quantum, there is always Szabo & Ostlund which has code you can refer to, as well as Levine. I am slightly divorced from the QM side of things so I don't have many other recommendations in that area. For statistical mechanics it starts and ends with McQuarrie for me. I have not had to understand much of it in my career so far though. I can also recommend the Oxford Primers series. They're cheap and make solid introductions/refreshers. I saw in another comment you are interested potentially in enzymology. If so, you could try Warshel's book which has more code and implementation exercises but is as difficult as the man himself.

Jensen comes closest to a detailed, general introduction from the books I've spent time with. Maybe focus on that first. I could go on for pages and pages about how I'd approach learning if I was back at undergrad so feel free to ask if you have any more questions.



Out of curiosity, is it DLPOLY that's irritating you so much?

u/AurelionStar · 1 pointr/Physics

For math there isn't much better undergraduate/beginning graduate review than Arfken, Weber, Harris. This will cover most mathematics you'll encounter in your first and maybe second years of graduate studies. Personally I'm not a huge fan of the complex contour integration sections you'll encounter in that book - I much prefer Ahlfors or Rudin for something more on the pure side or Churchill for something more on the applied side of complex analysis. The other sections are, in my opinion, stellar - although I have only the third edition in my possession.

u/gtani · 1 pointr/math

I looked at similar (WA resident also) but there's only a few community college classes that are interesting (linear algebra, probability, ODE) so then you're looking at UW/WSU tuition. There's a couple applied tracks you could consider: machine learning and financial math:

https://metacademy.org/roadmaps/

http://www.deeplearningweekly.com/pages/open_source_deep_learning_curriculum

https://www.quantstart.com/articles/Quantitative-Finance-Reading-List

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Self study: math for physics texts like Arfken/Harris/Weber, Boas, Riley/Hobson, Thomas Garrity

http://www.goldbart.gatech.edu/PostScript/MS_PG_book/bookmaster.pdf

https://www.amazon.com/Mathematical-Methods-Physicists-Seventh-Comprehensive/dp/0123846544